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Theory of Machine

Theory of Machine
Elements of pairs held together mechanically is known as

Open pair
Mechanical pair
Closed pair
Rolling pair

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Theory of Machine
Flexible coupling is used because

It transmits shocks gradually
It is easy to engage and disengage
It prevents shock transmission and eliminates stress reversals
It is easy to disassemble

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Theory of Machine
A disc is a spinning with an angular velocity ω rad/s about the axis of spin. The couple applied to the disc causing precession will be (where I = Mass moment of inertia of the disc, and ωP = Angular velocity of precession of the axis of spin)

(1/2).Iω²
(1/2). I ω ωP
Iω²
I ω ωP

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Theory of Machine
The Grubler's criterion for determining the degrees of freedom (n) of a mechanism having plane motion is (where l = Number of links, and j = Number of binary joints)

n = 3(l - 1) - 2j
n = 2(l - 1) - 2j
n = (l -1) - j
n = 4(l - 1) - 3j

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Theory of Machine
The essential condition of placing the two masses, so that the system becomes dynamically equivalent, is (where l₁ and l₂ = Distance of two masses from the centre of gravity of the body, and kG = Radius of gyration of the body)

l₁l₂ = kG²
l₁ = kG
l₁l₂ = kG
l₂ = kG

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Theory of Machine
The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line

Perpendicular to line as per (A)
Joining the corresponding points
At 45° to line as per (A)
Not possible to determine with these data

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